While I'm always complaining about the lack of finger friendly UI - here's few points I do agree about:

You'd lose handwriting recognition. While I never got it to work well for me, a lot of people have and love it.

You'd lose inking in Notes. The ability to add drawings in your notes makes them more useful.

Selection for copy/paste operations would be more difficult. That's probably one reason that Windows Mobile Standard and the iPhone don't have full-fledged copy/paste yet. You either need to switch into a selection or cursor mode (which wastes time) or have an on-screen cursor like regular Windows with a separate way to control it (using the directional pad means having a cursor mode).

Scrolling large distances is more difficult.

Drawing programs would be almost nonexistent. Trying to draw with your finger instead of a stylus is like comparing fingerpainting to ink sketches.

The learning curve could be worse for experienced Windows Mobile users. New users might like an exclusively finger-friendly interface, but some experienced users might not.